Asegment 12" long is divided into two segments having lengths in the ratio of 2: 3. find the length of the shortest segment.
2
2 2/5
4 4/5
7 1/5

4 4/5.
Divide 12 by 5, 5 because you would add 2 and 3
You will get 2 2/5
Now you know what the ratio 1 is equivalent to
There is 2 ratio portions in the shortest segment.
2 2/5 multiplied by 2 is 4 4/5

Let x and y be the lengths of the segments. From the given above, the ratio of the sides is equal to 2/3.
                                         x / y = 2 / 3
From the proportion, it is conclusive that x = 2y/3. The sum of x and y should be equal to 12.
                                        x + y = 12
                                     (2x/3 + y) = 12
The value of y is 7.2. The value of x then is equal to 4 4/5. The answer is the third choice.